Sun sensors and star sensors are two kinds of important celestial sensors and are widely used in many spacecrafts for attitude measurement. Sun sensors are a kind of attitude sensor for measuring the angle between the sun light and a certain axis or plane of a moving vehicle, and is widely used in many areas such as solar energy utilization and attitude control of spacecraft. New digital sun sensors mainly include: an optical mask with single pinhole or pinhole array, an image sensor such as CMOS (Complementary Metal Oxide Semiconductor) or CCD (Charge Coupled Device), and an information processing circuit.
The principle of a sun sensor is as follows: sun light is projected onto the image sensor though the pinhole on the optical mask and a spot is formed. The position of the spot changes with the incident angle of sun light. Then, spot image processing and attitude computing are executed by an information processing circuit, and finally, the attitude of the spacecraft is obtained.
A star sensor is a kind of high precision attitude measurement device for spacecraft that operates by observing stars. The principle of the star senor is as follows: a sky image is captured by an image sensor such as CCD or CMOS, and an image processing procedure is carried out to extract the centroid coordinates and brightness of the stars in the sky image. Next, a star identification program uses this information to find corresponding matches between measured stars (in sky image) and guide stars (in a star catalog). Finally a 3-axis attitude is obtained.
Before the celestial sensor is put into use, its internal parameters must be precisely calibrated to guarantee high measurement precision. The internal parameters include the focal length F of the optical system, an origin coordinate where the optical axis crosses the image sensor (also called as main point) and distortion coefficients, etc. The calibration of such internal parameters is referred to as celestial sensor calibration. Currently, there are two kinds of calibration methods. The first method is to utilize real sunlight or starlight and perform data acquisition and calibration. The second method uses a celestial simulator to provide simulated sunlight or starlight, and performs data acquisition and calibration with the help of a rotator. For the latter, only the focal length F and the main point coordinate are used in the calibration model, and the calibration precision is higher than the former. Further, the calibration process is more convenient. However, there are some disadvantages with this method.
For example, the sunlight or starlight vector from the celestial simulator is not strictly vertical to the plane formed by the two rotation axis of the rotator coordinate frame. Moreover, there is installation error between the celestial sensor and the rotator, such that the celestial sensor coordinate frame can not be identical to the rotator coordinate frame. Because of those external factors, such as installation error and adjustment error, there is error in the calibration method which uses only internal parameters in imaging modeling of celestial sensor. Therefore, the precision of estimation of internal parameters is influenced.
Generally, there is nonlinear distortion in the pinhole imaging model of the celestial sensor. So, errors are introduced into the calibration method which only includes internal parameters of the focal length F and the main point coordinate.